Curve fitting with pure fluid amplifiers



Aug. 19, I969 c. v. DI CAMILLO 3,461,399 CURVE FITTING WITH PURE .FLUIDAMPLIFIERS Filed Oct. 6, 1966 a Sheets-Sheet 1 VARIABLE FLUID IBPUTINVENTOR CARMINE V. DI CAMILLO M, V0 M g V ATTORNEYS C. V. DI CAMILLOFiled 001:. e. 1966 wwzw PIN

P OUT- 5 Sheets-Sheet 2 7 P IN OUT T P IN .FmAC

P I} P IN PIN INVENTOR ATTORNEYS 8- 19, 1959 c. v. DI CAMILLO. 3,461,899

CURVE FITTING WITH PURE FLUID AMPLIFIERS Filed Oct. 6. 1966 I I 3Sheets-Sheet 5 T "l3l3 I I v B O l '0) I2I3 Ian I2II i Q INPUT PRESSURE506 505 503 K .fr 500 BISTABLE BIAS VARIABLE 7 INPUT 1 PbwER mvsmoxSOURCE CARMINE v. 0| CAMILLO ATTORNEYS United States Patent 3,461,899 aCURVE FITTING WITH PURE .FLUID AMPLIFIERS Carmine V. Di Camillo, SilverSpring, Md., assignor to Bowles Engineering Corporation, Silver Spring,Md., a corporation of Maryland Filed Oct. 6, 1966, Ser. No. 584,814

A Int. Cl. FlSc 1/10 U.S. Cl.13781.5 '15 Claims ABSTRACT OF THEDISCLOSURE ,Afluid. function generator is capable ofapproximating-virtually any output signal versus input signal functionby utilizing a first fluidic amplifier fed by the input signal and by anoutput signal from a second fluidic amplifierwhich is also fed by theinput signal. The second amplifier thus provides a variable bias signalto the first, the bias. changing in response to the input signal inaccordance with the gain" characteristic of the second am- Patented Aug.19, 1969 ice v embodiment of FIGURE 5.

' In order to facilitate an understanding of the particular embodimentsillustrated and to be described herein, it is first necessary tounderstand the operation of the pure fluid amplifier elements employedin these embodiments; The following description is of only one suchelement and two of the subsequently described'embodiplifier. Tailoringthe gain characteristic offlthe second amplifier, as by fixed biassignals, determines the effectiveness of the variable bias signal at thefirst amplifier over specified input signal ranges.

This invention relates to pure fluid systems in general and, morespecifically, to curve-fitting techniques employing pure fluidamplifiers in a cascaded network, In pure fluid systems, it is often arequirement that an output signal be some specified non-linear functionof a variable input signal. The non-linear function may be some idealmathematical curve or some arbitrary curve resulting from certainpractical considerations, but in either case, a fluid device capable ofresponding to an input signal in accordance with said function is usefulin pure fluid computers, control devices, etc.

It is therefore an object of this invention to provide a devicecomprising a plurality of interconnected pure fluid amplifiers whichproduce a predetermined non-linear output signal in response to avariable input signal. r

It is another object of this invention to provide a technique forutilizing a plurality of pure fluid amplifiers to achieve substantiallyany desired non-linear output versus input characteristic in a purefluid device. a It is still another object of this invention to providea methodof matching the output versus inputcharacteristic of a purefluid device to any predetermined nonlinear curve. v

It is yet another object of this invention to provide a method ofinterconnecting a plurality of pure fluid amplifiers so as to produce apure fluid device having a predetermined non-linear output versusv inputcharacteristic.

mentsemploy only that element. This, however, it is not to be'construedas limiting the scope'of this'invention to the use of only said element,for it will be readily apparent that various different types of fluidamplifiers may be used in various combinations to achieve particularoutput versus input characteristics. With this in mind, reference ismade to FIGURE 1 wherein a particular pure fluid amplifier 10 of thestream interaction type and designed to operate in the analog mode isillustrated. In

this type of amplifier, a power nozzle issues a stream of fluid into aninteraction region or chamber. A control nozzle issues a control streamof fluid which impacts against and deflects the power stream away fromthe control nozzle. There is a conservation of momentums between the twostreams and, therefore, the power stream is deflected at the point ofimpact from its original direction of flow through an angle which is afunction of the momentum of the power stream and the momentum of thecontrol stream. In this manner, a low energy control stream of fluid maybe utilized to direct a high energy power stream of fluid toward or awayfrom a target area or receiving aperture system, this constitutingamplification.

Amplifier 10 comprises a power nozzle 11 and two left control nozzles 13and 15, and two right control noz log operation of amplifier 10. 1

I radially displaced to the left and right of the axis of Still anotherobject of this invention is to provideta pure fluid'device having apredetermined non-linear output versus input characteristic bysuperimposing on one another the output versus. input characteristics ofa plurality of pure fluid amplifiers. v

I The above and still further objects, features and ad vantages of thepresent invention will become apparent upon consideration of thefollowing detailed description of severalspecific embodiments thereof,especially when taken in conjunction with the accompanying drawings,wherein: u

FIGURE 1 is a plan view ofa purerfluid amplifier which is utilized insome of the embodiments of this invention; Y

FIGURE 2 is a plot of the output versus input characteristic of theamplifier of FIGURE 1; A

power nozzle 11. Connected between power nozzle 11 and control nozzle 17is restrictor 33 which also communicates with valve 35 at the end of therestrictor remote from power nozzle 11. It should 'be apparent from thesubsequent" description that restrictor 33 need not be employed forparticular embodimentsof this invention, and in the' alternative,additional restrictors of various pressure-dropping capability may beemployed between the power nozzle 11 and any one ormore of the controlnozzles 13, 15, 17 and 19.

In describing one possible mode of operation of amplifier 10, it will beassumed thata first source of fluid under constant pressure (notillustrated) is coupled to power nozzle 11. In addition to creating apower stream in chamber 21, this source results in a bias flow, of loweradjustable external bias signal may be coupled to nozzle 17 ifdesired.thereby eliminating the necessity for restrictor 33 and valve 35. It isassumed, for purposes of the following discussion, that control nozzles15 and 19 and output passage 29 are vented to a suitable fluid dump,that a variableepressure input signal (not illustrated) is supplied tocontrol nozzle 13, and that suitable loads or utilization devices (notillustrated) are connected to output passages 27 and 31.

It may be noted that the power stream of fluid from power nozzle 11,when it arrives at the ingress orifices of the output passages 27, 29and 31, has a transverse pressure gradient. The center of the stream isat a maximum pressure, while the boundary regions of the stream, due tomomentum interchange with the ambient fluid, are at a lesser pressure.The Width of the orifices of passages 27, 29 and 31 are here shown ofsuch a size that each samples a small transverse portion of the powerstream; If the power stream is axially centered on the orifice ofpassage 27, maximum pressure is developed at that passage. If the powerstream is not directed at the center of the orifice of passage 27, thena lesser pressure is developed thereat. If the power stream is notimpinging on the orifice of passage 27, then no significant pressure isdeveloped at that passage. The fluid from the power and the controlstreams which does not pass into the passages 27, 29 or 31 is divertedto the regions 23 and 25 and is dumped through the fluid aperturestherein which communicate with the atmosphere.

As previously stated, the hypothesized input signal for the apparatusillustrated in FIGURE 1 is applied to the control nozzle 13 and theoutput signal is taken from the right output passage 31. Thus, there isa positive relation between the input and the output signals; that is,the greater the input signal or pressure from the nozzle 13, the greaterthe deflection of the power stream towards the passage 31, and thegreater the signal or pressure developed at a utilization deviceconnected to passage 31.

Referring now specifically to FIGURE 2, under the conditions assumedabove, curve a represents the output signal pressure at output passage31 as a function of input signal pressure to control nozzle 13. Curve Brepresents the output signal pressure at output passage 27 as a functionof input signal pressure to control nozzle 13. It is seen that curves Aand B are non-linear at their extremities (minimum and maximum inputpressures). This is due to the fact that the velocity profile of thepower stream at the distances of the output passages from the powernozzle employed herein is a bell-shaped curve, symmetrical about thelongitudinal axis of the stream. The reason for this may best beunderstood by considering the velocity profile (velocity as a functionof distance transversely of the power stream axis) of the power stream.Upon reaching the ingress orifices of the output passages, the fluid atthe boundaries of the power stream is flowing at a velocity which isslightly greater than that of the ambient fluid. The fluid at the centerof the stream is flowing at a somewhat greater velocity, representingthe maximum velocity of the stream. The slope of the curve betweenmaximum and minimum velocities is not a straight line but rather morelike a bell-shaped curve which rises gradually at first, thereafterrising rapidly through a center region of the stream over which regionthe curve levels off. The curve is symmetrical about the longitudinalaxis of the power stream. Since, as mentioned above, the relativelynarrow output passage orifices sample various portions of the powerstream as the stream is deflected, these orifices are exposed to streamvelocities which vary in accordance with stream deflection. Since eachoutput passage receives fluid from a different region of the stream asthe input signal varies, and since these regions have velocities whichare defined by the bellshaped velocity profile of the stream, the outputsignal pressure must follow the velocity profile curve of the stream asa function of input pressure. Thus, the curve A of FIGURE 2 is a plot ofone-half of the velocity profile of the stream while curve B is a plotof the other half of the stream.

The shapes of curves A and B may be altered by varying the bias pressurelevels at control nozzles 15, 17 and 19. For example, if the pressure atnozzles 17 or 19 is increased, a greater input pressure at nozzle 13 isrequired to deflect the power stream toward output passage 27 from itsinitial direction. As a result, the initial-portions of the outputcurves tend to flatten somewhat as represented by dotted curves A and B.Decreasing the pressure at nozzle 15, as by suction or similar means,brings the same curve-flattening result. On the other hand, by makingthe pressure at nozzle 15 larger than the combined pressure at nozzles17 and 19, the quiescent conditions can be reversed, with the powerstream becoming normally directed toward output path 31. Obviously, theoutput signals can be made quiescently equal by equalizing oreliminating the bias signals, or by appropriate design of the amplifierconfiguration.

Another method of changing th shape of curves A and B involves feedingback one of the output signals, for example, the signal at outputpassage 31, to one of the control nozzles, for example, 15, in a mannerdescribed in co-pending application by D. R. Jones, Ser. No. 413,267,filed Nov. 23, 1964, Said application discusses a number of techniquesfor linearizing the gain characteristic of amplifiers such as 10, all ofwhich are applicable to effect various shaped characteristics forpurposes of this application.

Another manner in which the characteristic of the amplifier may bere-shaped is by applying to the control nozzles bias pressure signalswhich themselves vary as functions of the input signal. Suchinput-responsive bias signals may be generated by other fluid amplifiershaving output versus input characteristics shaped in accordance with theprinciples discussed above. Thus, a cascaded group of such amplifierscan be employed to produce output versus input curves of substantiallyany shape. Three embodiments employing this principle are describedbelow.

FIGURE 3 illustrates a device whereby a group of pure fluid amplifiers,such as amplifier 10 of FIGURE 1, are interconnected so as to produce anoutput pressure signal which varies approximately as the square root ofthe input pressure signal. The device comprises four cascaded fluidamplifier stages 110, 210, 310 and 410 with the individual elements ofeach amplifier being designated by the same reference numerals employedfor like elements in FIGURE 1 but preceded by the numbers 1, 2, 3 or 4to indicate to which amplifier stage the elements belong. All fourstages have their power nozzles 111, 211, 311 and 411, respectively,connected to a constant pressure fluid power source (not illustrated).It is to be noted that system requirements may demand that differentpressures be applied to the various power nozzles; thus, the nozzles mayeach be connected to individual constant pressure sources or preferablyto a common constant pressure source via individual pressure droppingflow restrictors similar to restrictor 33 in FIGURE 1.

Control nozzles 119, 219, 319 and 419 are connected to a common ductwhich conveys a fluid input signal of varying pressure to said nozzlesfrom some input signal source 101. Control nozzles 115, 117, 217, 317and 415 are vented to a suitable fluid dump, while control nozzles 113,215, 315 and 417 are connected via respective pressure dropping flowrestrictors 133, 233, 333 and 433 to the constant pressure power source(not illustrated) associated with each of the respective stages. Outputpassages 127, 129, 227, 229, 327, 329*, 429 and 431 are vented to asuitable fluid dump. Output passage 131 of first stage is connected tocontrol nozzle 213 of second stage 210. Similarly, output passages 231and 331 are connected to control nozzles 313 and 413, respectively.Output passage 427 of the final stage 410 is the output of the overalldevice and is connected to a suitable load or utilization device (notillustrated).

The operation of the embodiment illustrated in FIG- URE 3 of theaccompanying drawings is most readily understood when considered inconjunction with the input-output curves for stages 110, 210, 310 and410, as illustrated in FIGURES 3A, 3B, 3C and 3D, respectively.Referring first to stage 110, FIGURE 3A represents a plot of thepressure output signal P appearing at output passage 131 as a functionof a variable pressure input signal X applied at control passage 119 andoriginating at source 101. This plot may be represent d by the followingmathematical expression:

where A is the gain of amplifier stage 110, C is the constant pressuresignal appearing at control nozzle 113, responsive to flow restrictor133, and X is the variable pressure input signal appearing at controlnozzle 119. In the following description, the assumption is made thatgain A (as well as gains A A and A of stages 210, 310, and 410,respectively) is constant over the range of input pressures beingconsidered, which means that the gain characteristic for each amplifieris considered as being linear as opposed to the actual non-linearcharacteristic illustrated as curve B in FIGURE 2. The prac-. ticaleffects of this assumption are discussed in detail following the ensuingdescription of the operation of the device of FIGURE 3.

Under quiescent conditions (X=), the only control signal acting on thepower stream of stage 110 is constant pressure bias signal 0, at controlnozzle 113. The level of C is such (as adjusted by throttle 35 of FIG-URE 1) that when no other control signal is present, the power stream isdirected along the centerline of passage 131, so as to produce a maximumpressure signal thereat. This quiescent output signal has a value A C asfound by setting X equal to 0 in Equation 1. As X assumes pressurelevels greater than zero, the signal at control passage 119 opposes theconstant pressure at nozzle 113 and deflects the power stream away fromout-. put passage 131 and towards passages 129 and 127. As illustratedby FIGURE 3A and by theA X factor of Equation 1, this increase in X ismanifested by a pressure decrease from the A C maximum level at outputpassage 131, such decrease being proportional to the magnitude of theincrease in X. As X increases further, the power stream is deflectedfurther towards passages 127 and 129 and P continues to decrease inproportion to the increase in X. When X becomes equal to C P becomessubstantially equal to zero because the power stream receives equal butopposite pressures from control nozzles 113 and 119 so thatsubstantially the entire power stream is directed to vented outputpassage 129. For values of X above C the power stream is directed stillfurther away from output passage 131 and signal P therefore remainszero. Referring now to amplifier stage 210 and the output versus inputcharacteristic in FIGURE 3B for the output signal P at passage 231, thefollowing mathematical relationship may be derived for P for 05X 3Cwhere A C and X are as defined above, A is the linearly approximatedgain of stage 210, and'C is the value of the constant pressure signalcreated at control nozzle 215' by flow restrictor 233. The componentparts of the righthand side of Equation Zrepresent the signals appearingat the various control nozzles of stage 210. For example, the A (C X)term is actually P as defined in Equation 1 and is provided at controlnozzle 213 from output passage 131 of stage 110; the C term is theconstant pressure signal at control nozzle 215, as defined; and X is thevariable input signal appearing at control nozzle 219. When X is at zeropressure, P becomes equal to A (A C +C a constant pressure levelresulting from the power stream deflection caused by two aiding pressuresignals; namely, A C at nozzle 213 and C at nozzle 215. C is adjusted sothat for quiescent conditions (X :0) the power stream of stage 210 isdirected along the centerline of output passage 231. This produc smaximum output pressure under quiescent conditions. As X increases, theP signal appearing at control nozzle 213 decreases as illustrated inFIGURE 3A and signal C at nozzle 215 remains the same, resulting in anet control pressure decrease on one side of the power stream.Similarly, the increasing X signal causes increasing pressure on theopposite side of the power stream. These effects on opposite sides ofthe power stream are additive to cause the power stream to be deflectedaway from passage 231 at a faster rate with respect to increases in Xthan would be the case if only the X signal, or if only the A X signalwere applied to their respective control nozzles. Thus, the slope of thecurve in FIGURE 3B is comparatively large (more negative) relative tothe slope of the curve 3A for values of X between zero and C Thiscomparatively large slope may be represented mathematically as A (A +1),obtained by multiplying Equation 2 through for the coefficient of X. Asdescribed above, when X becomes equal to C P is substantially zero andthus there is no signal at control nozzle 213. By substituting C for Xin Equation 2, it is discovered that when X=C P is equal to A (C C As Xincreases above C P decreases from this A (C C value at a rate somewhatless than the rate of decrease experienced for increasing values of X inthe range 0511563. This is true since the increasing power streamdeflection effect of signal X at control nozzle 219 is no longer aidedby a decreasing deflection effect at nozzle 213 when X is greater than CIn fact, the slope is determined entirely by A in this region as opposedto the A (A +1) slope for values of X less than C This is bestillustrated by considering the following mathematical expressiondefining P231 for the region C X5C It is apparent from Equation 3 thatthe slope in this region (the coefficient of X) is equal to A and it isalso apparent that for X =C the value of P becomes zero. This latterfact is to be expected since when the pressure at control nozzle 219 (X)is equal to the pressure at control nozzle 213 (C and the pressures atnozzles 215 and 217 are zero, substantially the entire power stream isdirected toward vented output passage 229, thereby rendering thepressure level at output passage 231 substantially zero.

Amplifier stage 110 cuts off at values of X above C such that it nolonger aflectsstage 210. This causes a change in the rate of decrease ofoutput pressure at'passage 231 of stage 210. In a similar manner, it canbe demonstrated that the gain characteristic of amplifier stage 310exhibits three different slopes in three respective regions of valuesfor the same region of AX. Specifically, it is noted that stage 310receives three input signals; namely, P at control nozzle 313, aconstant pressure signal defined as C, at nozzle 315, and X at nozzle319. When X=0, the only signals having any effect on deflecting thepower stream of stage 310 are P which has a value A (A C '+C asdescribed above and C which may be adjusted such that the combinedeffect of both signals deflects the power stream so as to be directedalong the centerline of passage 331. This produces a maximum quiescentpressure level, at pas- Sage Of A3AZ(A1C1'+CQ)+A3C3, where'Ag IS theapproximated constant gain of amplifier stage 310. As illustrated inFIGURE 3C, which is the gain characteristic for stage 310 with respectto the output signal at pas sage 331, increasing values of X produce arelatively steep rate of pressure decrease at passage 331 from theaforementioned quiescent level. This relatively steep decrease rateoccurs because of the aiding eflects of an increasing pressure in signalX at nozzle 319 and a decreasing pressure in signal P at nozzle 313i Forvalues of X below 0,, P is controlled by the larger of its twocharacteristic slopes, this resulting from the abovedescribed effectwhich signal P from stage 110 has on signal P When X is greater than Cstage 110- has been shown to be cut-off and P has been shown to reflectthis cut-off condition by exhibiting a smaller slope. Thus, thedecreasing P signal at nozzle 331 still aids the increasing X signal atnozzle 319 for values of X greater than C but the aiding effect is notas pronounced for a given change in X as was the case for values of Xless than C and the gain characteristic for P in FIG- URE 3C exhibits alesser slope in the region of X values above C than in the region of Xvalues below C As Was previously noted, stage 210 cuts off at values ofX above C which causes the P signal applied to nozzle 313 to assume azero value. Thus, for values of X above C there is no variable controlsignal applied to stage 310 except signal X at nozzle 319. With X actingalone, unaided by a decreasing P signal, the rate at which the powerstream is deflected with respect to changes in X is substantially lessthan for lower values of X. Thus, as illustrated in FIGURE 3C, P dropsoff at a still lesser rate as X increases in the range of X values aboveC than was the case for values of X between C and C This still lesserrate continues for increasing values of X until X equals C at which timethe control pressure from nozzle 319 balances that from 315 andsubstantially the entire power stream is directed towards vented passage329, thereby producing essentially zero output pressure at passage 331.

In a manner similar to that described above in which the gaincharacteristic for stage 310 was illustrated as exhibiting threedistinct slopes in three different regions of X values, it can bedemonstrated that stage 410 has a gain characteristic exhibiting foursuch different slopes, as illustrated in FIG. 3D. Specifically, thecontrol signals applied to stage 410 comprise P at nozzle 413, C, atnozzle 417, and X at nozzle 419. When X=O, only signals P and C act todeflect the power stream of stage 410, and these signals producepressures which are opposite insofar as their effect on the power streamis concerned. Since we are attempting to provide an output signal P atpassage 427 which represents the square root of X, it is desirable thatP be equal to zero when X is zero. Thus, the quiescent value (for X ofthe signal P must be greater than C, and such that the power stream isdeflected away from passage 427. This may be accomplished by adjustingrestrictor 433 accordingly as described in relation to element 35 ofFIGURE 1. In fact, since the square root curve rises sharply for lowvalues of X, the relative pressures of the quiescent P and C, have a neteffect of directing the power stream somewhat towards vented passage 429but such that the slightest pressure increase in signal X at nozzle 419produces a discernible pressure at passage 427. Thus, as X increases inthe range 05X C there is a sharply sloped pressure signal response atpassage 427 corresponding to the aiding effect of increasing pressure(signal X) at control nozzle 419 and decreasing pressure (signal Poperating in the region in which it exhibits the greatest slope) atnozzle 413. For values of X greater than C butless than C the effects ofstage 110 are no longer present, thus signal P decreases at a lesserrate for increasing X and the output signal P continues to increase butat a somewhat lower rate. For C 5X C amplifier stage 210 no longer hasany effect on signal P and P exhibits a still lesser slope. For valuesof X above C P is zero and the only effective variable signal is Xitself. Thus, increases in X above C still produce changes in P but at astill further reduced slope.

The curve of FIGURE 3D approximates the square root curve in that outputsignal P rises sharply for increases in X at low levels of X, andcontinues to rise but at a decreasing rate for higher values of X. Infact, the curve of FIGURE 3D resembles a piecewise linear approximationof the square root curve. In describing the operation of the circuit ofFIGURE 3, it was assumed that the various amplifier characteristics wereentirely linear, thereby ignoring the nonlinear portions of curve B inFIGURE 2, in order to facilitate an understanding of the operation ofthe circuit. These non-linear portions tend to smooth out the piecewiseaspects of the curves in FIG- URES 3A through 3D so as to produce acurved transition between each segment of the curve and provide an evencloser approximation of the square root function, for the followingreasons: Since the values of C C and C are chosen such that thequiescent values of output signals P P and P respectively, lie at thepeak portion of characteristic curve B in FIGURE 2, the respectiveoutput signals exhibit non-linear gain characteristics at theirextremities as exhibited by curve B at its extremities. Specifically, inFIGURE 3A, P becomes somewhat asymptotic as it approaches zero in thesame manner as curve B smoothes, and thus the sharp transition at C inFIGURE 3A is in reality a smooth transition under actual conditions.Similarly, the sharp transitions occurring at points C C C and C inFIGURES 3B, 3C and 3D are in reality smoothed by the upper and lowernonlinear portions of curve B so that the output versus inputcharacteristic for P really is a smooth curve rather than the piecewiselinear approximation of FIGURE 3D.

The above description is not intended to limit quiescent conditions inall possible embodiments which may employ the inventive conceptsdisclosed herein. For example, the

power streams for stages 110, 210 and 310 do not necessarily have to bequiescently directed along the centerline of respective output passage131, 231 and 331, but rather may be somewhat displaced from thecenterline such that the quiescent output signals are not representativeof the maximum amplifier output level. This scheme does not utilize eachstage to its full amplification capability, but nevertheless, hasutility in particular applications.

A particular application of the square root circuit might be subject tosystem limitations with respect to permis sible output signal levels,etc. The signals in the embodiment of FIGURE 3 may be scaled accordinglyby changing the power stream pressure in one or more stages, anexpedient which reduces the output signal level but which does notaffect the shape of the output versus input characteristic.'As discussedpreviously, the power stream pressure may be made different in eachstage by means of a series of adjustable restrictors or by utilizingseparate fluid pressure sources.

In the above-described embodiment, it is preferable to include anadjustment means such as valve 35 of FIG- URE 1 in conjunction withrestrictors 133, 233, 333 and 433 so as to provide a trim control forbetter approximation of the square root curve.

The embodiment of FIGURE 4 demonstrates a more general application ofthe principles of this invention. This embodiment has an output versusinput characteristic approximating'an arbitrary curve such as that ofFIG- URE 4A which maybe any theoretically or experimentally obtainedcurve. In FIGURE 4, four fluid amplifiers 1110, 1210, 1310 and 1410 areillustrated, the individual elements of each being designated byreference numerals corresponding tothose for respective elements inFIGURE 1 but having the numerals 11, 12, 13 or 14, respectively prefixedtherebefore to indicate the amplifier to which the element belongs.

The various power nozzles 1111, 1211, 1311 and 1411 of eachamplifierstage are connected to respective con'-' stant pressure fluid powersources (not illustrated). Control nozzles 1113, 12 13 and 1313 are alsoconnected to these respective power sources via pressure dropping sage1331,.andcontro1 nozzle 1413 is connected to output passage 1131. Outputpassage 1427 comprises the output for the overall device and isconnected to a suitable load or utilization device (not illustrated).The remaining control nozzles and output passages are vented to suitablefluid dumps.

In considering the operation of the device of FIGURE 4, it will beassumed that the bias signal applied to control nozzle 1213 viarestrictor 1233 is at a relatively high pressure, that the bias appliedto control nozzle 1113 via restrictor 1133 is at a relatively lowpressure, and that the bias applied to control 1313 via restrictor 1333is at some moderately nominal pressure intermediate that the other twobias signals. Under these conditions, the input signal at control nozzle1219 must become relatively large before it has any effect on the outputof stage 1210 and therefore the gain curve for output passage 1231 asillustrated in FIGURE 4D has a relatively flat portion for low values ofinput signal, and gradually assumes the normal amplifier characteristiccurve as the input becomes larger. Similarly, a high input signal atcontrol nozzle 1319 will overcome the moderate bias at nozzle 1313 tosubstantially deflect the power stream and minimize the output signal atpassage 1331 of stage 1310. Since the input signal to nozzle 1319 isreally the output signal from passage 1231, this input is quite high forlow values of signal from input source 1001, as indicated by the curveof FIGURE 4D. Thus, the power stream is deflected away from-passage 1331until the signal from source 1001 increases to the level at which theoutput of passage 1219 (FIGURE 4D) becomes low enough to permit the biassignal at nozzle 1313 to begin to deflect the power stream in amplifier1310. As illustrated in FIGURE 4C, this results in an outputcharacteristic curve for passage 1331 which is minimal and flat for mostof the lower and middle region input pressures, and which begins toassume the normal amplifier characteristic curve at some relatively highinput pressure.

Since the bias at control nozzle 1113 of amplifier 1110 is relativelylow, relatively low input signal pressures at control nozzle 1119 willeflect a change in the power stream direction. As a result, the gaincharacteristic for output passage 1131 of amplifier 1110 hassubstantially no flat portion for small values of input signal anddecreases rather rapidly until it levels off at some minimal value asillustrated in FIGURE 4B.

The output stage 1410 of the device of FIGURE 4 is controlled by threesignals which vary as a function of the input signal at source 1001. Thesignals are: the input signal at some reduced level which is applied tonozzle'1417 via restrictor 1005; the signal from output passage 1131which is applied to nozzle 1413 and which responds to the input signalfrom 1001 in a manner defined by the curve of FIGURE 4B; and the signalfrom output passage 1331 which is applied to nozzle 1419 and responds tothe input signal from source 1001 in a manner defined by the curve ofFIGURE 4C. Thus, for a zero input signal level, the minimal output fromamplifier 1310 at nozzle 1419 has substantially no effect on the powerstream of amplifier 1410, the high output from amplifier 1110 at nozzle1413 tends to deflect the stream away from output passage 1427, and theinput signal itself at nozzle 1417 is, of course, zero and has noeffect. Upon gradual increase of the input .pressure from source 1001,

the signalat nozzle 1419' (FIGURE 4C) remains minimal and. haslittleeflect, but the signal at nozzle 1417 increases while the outputof amplifier 1110 at nozzle 1413 decreasesso that both signals act toreduce the deflection of the power stream away from output passage 1427.As illustrated in FIGURE 4A, the output characteristic curve for passage1427 has-a rather steep slope for low level input signals,. reflectingthe aiding eflect of the two signals just described. As the input signalis increased further, the output of amplifier 1110 begins to level offat some minimalvalue (FIGURE 4B) so that the signal at nozzle 1413produces little effect on the power stream. Since the signal fromamplifier 1310 remains minimal for these input levels, the only signalwhich has substantial eflect on the power stream is the signal at nozzle1417. Thus, as the input signal increases through this region, thenormal characteristic of the amplifier 1410 dominates, resulting in alesser slope for this portion of the characteristic curve (FIGURE 4A)than for the previous portion. If the input signal is increased stillfurther, the output from amplifier 1110 remains minimal and relativelyineflective at nozzle 1413, but the output of amplifier 1310 at nozzle1419 increases in a manner to aid the input signal at nozzle 1417 indeflecting the stream toward output passage 1427. The result is asteeper output slope for this section of the gain characteristic ofamplifier 1410. The embodiment of FIGURE 4 has actually been constructedto match the experimentally obtained flow characteristics of aparticular valve, said characteristics being represented in FIGURE 4A.

The technique employed above; namely, the superposition of portions ofthe characteristics of a plurality of interconnected pure fluidamplifiers, can similarly result in a device having substantially anydesired output versus input characteristic. The use of adjustablerestrictors enables one to trim the various stages to more closelyapproximate the desired overall curve. In addition, where the devicerequires a relatively large number of amplifiers to achieve a particularcharacteristic shape but does not require the overall gain inherent inthe use of such a number of amplifiers, restrictors may be used to scaledown the power stream pressure, the various control pressures, and theinput pressure as necessary. Various other expedients, such as feedback,are also contemplated in obtaining desired results.

While the above-described embodiments utilize only one specific type ofpure fluid amplifier, the invention described herein is not intended tobe so limited. Any type of pure fluid amplifier, whether of the streaminteraction type, the boundary layer eflect type, the vorteX type, etc.may be employed in various combinations to achieve specific gaincharacteristics. For example, the rather simple device schematicallyillustrated in FIGURE 5 makes use of a bistable fluid amplifier 500having one of its output passages 501 connected to a control nozzle 513of an analog amplifier 510. These amplifiers may be of any appropriatetype so long as they are designed to operate bistably in the case ofamplifier 500 and in an analog manner in the case of amplifier 510.Respective constant pressure fluid sources are applied to the powernozzles 502 and 512. A variable pressure input signal from some externalsource such as 520 is connected to control nozzles 503 and 513 of therespective amplifiers. Control nozzle 504 of amplifier 500 is connectedto a suitable bias pressure. Output passage 506 of amplifier 500 isconnected to control nozzle 514 of amplifier 510. Out- .put passage 515of amplifier 510 provides the output forthe overall device and may beconnected'to a suitable load or utilization device (not illustrated).

The nature of bistable amplifier 500 is such that the power stream willnormally be deflected to output passage 506 in the absence of any inputsignal at nozzle 503. As the level of the input signal is increased, thestream remains so deflected until the input reaches some pre determinedthreshold pressure, at which time the stream rapidly switches to outputpassage 505. The switching threshold is determined by various factorssuch as amplifier physical configuration, bias level at nozzle 504, andthe like; The resulting output versus'input characteristic of amplifier500 therefore is step-shaped as illustrated in FIGURE 5A which is thecharacteristics for output 506.

The gain characteristics for outputs 515 and 516 of amplifier 510 areillustrated in FIGURE 5B and 5C, respectively. The dotted portions ofthe curves represent the natural amplifier characteristics for an inputat nozzle 513 Without the influence of any signal at control nozzle 514.As is evident, these curves are somewhat similar to curves A and B inFIGURE 2. The effect on the characteristics of connecting the output atpassage 506 from amplifier 500 to nozzle 514 is illustrated by the solidlines in FIGURES 5B and 5C. Since, for values of input signal below thepredetermined threshold, there is a high level signal at nozzle 514,substantially all of the power stream of amplifier 510 is deflectedtowards passage 516. If this signal at nozzle 514 is made quite largerelative, to the expected range of input levels, the input signalproduces no effect on the stream so long as the input signal from source520 remains below the predetermined threshold. Once the input exceedsthe threshold, however, amplifier 500 is switched such that output 506is at substantially zero pressure, and amplifier 510 is then controlledsolely by the input signal at nozzle 513. Thus, for signals above thethreshold of amplifier 500, the output characteristic for amplifier 510is the normal characteristic of said amplifier unaffected by biassignals.

It is readily seen from the embodiment just described that even gaincharacteristics having discontinuities or steps therein can be designedinto a device comprising conventional fluid amplifiers. It should bepointed out that characteristics of more complex shape, including curvesexhibiting hysteresis effects (plural values of output pressure for anyparticular input pressure) are possible by merely employing theappropriate amplifier components appropriately interconnected.

I claim:

1. A fluidic device for producing an output pressure signal whichresponds to a variable-pressure input signal as a predeterminednon-linear function of said input sig nal, comprising:

a first pure fluid amplifier comprising a power nozzle,

a plurality of control nozzles, and a plurality of output passages, andhaving a pressure gain characteristic of which at least a first portion,as defined by a range of input pressures, is substantially differentfrom a corresponding first portion of said predetermined non-linearfunction;

means providing a source of fluid at constant pressure at said powernozzle;

means for connecting said input signal to a first of said controlnozzles;

variable bias means responsive to said input signal for modifying saidfirst portion of said gain characteristic to substantially conform tosaid corresponding first portion of said predetermined non-linearfunction;

means for connecting said variable bias signal means to at least asecond of said control nozzles;

wherein said variable bias means comprises at least a second pure fluidamplifier.

2. The device of claim 1 further comprising fixed bias means connectedto said second pure fluid amplifier for rendering it ineffective tomodify a second portion of said gain characteristic.

3. The device of claim 2 further comprising additional fixed bias meansconnected to said first pure fluid amplifier for modifying a portion ofsaid gain characteristic to conform to a corresponding portion of saidnon-linear function.

4. A fluidic device for producing an output pressure signal whichresponds to a variable-pressure input signal as a predeterminednon-linear function of said input signal, comprising:

a first pure fluid amplifier comprising a power nozzle, a plurality ofcontrol nozzles, and a plurality of output passages, and having apressure gain characteristic of which at least a first portion, asdefined by a range of input pressures, is substantially different from acorresponding first portion of said predetermined non linear function;

means providing a source of fluid at constant pressure at said powernozzle;

means for connecting said input signal to a first of said controlnozzles; i

variable bias means responsive to said input signal for modifying saidfirst portion of said gain characteristic to substantially conform tosaid corresponding first portion of said predetermined non-linearfunction;

means for connecting said variable bias signal means to at least asecond of said control nozzles;

wherein said gain characteristic has a plurality of pottions, as definedby a respective plurality of input pressure ranges, which differsubstantially from respective corresponding portions of said non-linearfunction, and further comprising: I g

a plurality of variable bias means for modifying said plurality ofportions of said gain characteristic to substantially conform to saidrespective corresponding portions of said non-linear function;

means for connecting said plurality of variable bias means to at leastone of said control nozzles.

5. The device of claim 4 wherein said plurality of variable bias meanseach comprise a pure fluid amplifier.

6. The device of claim 5 further comprising an adjustable fixed biasmeans connected to each of said pure fluid amplifiers for controllingthe effect produced by each variable bias means on said gaincharacteristic.

7. A fluidic device for producing an output pressure sig nal whichresponds to a variable-pressure input signal as a predeterminednon-linear function of said input signal, comprising:

a first pure fluid amplifier comprising a power nozzle,

a plurality of control nozzles, and a plurality of output passages, andhaving a pressure gain characteris tic of which at least a firstportion, as defined by a range of input pressures, is substantiallydifferent from a corresponding first portion of said predeterminednon-linear function;

means providing a source of fluid atconstant pressure at said powernozzle; Y

means for connecting said input signal to a first of said controlnozzles; variable bias means responsive to said input signal formodifying said first portion of said gain characteris tic tosubstantially conform to said corresponding first portion of saidpredetermined non-linear function; means for connecting said variablebias signal means to at least a second of said control nozzles;

wherein said predetermined non-linear function is the square rootfunction, and wherein said variable bias means comprise three cascadedanalog pure fluid amplifiers responsive to said input signal to modifysaid gain characteristic to conform substantially to said square rootfunction.

8. A fluidic device for producing an outputpressure signal whichresponds ot a Variable-pressure input signal as a predeterminednon-linear function of said input signal, comprising: I

a first pure fluid amplifier comprising a power nozzle,

a plurality of control nozzles, and a plurality of output passages, andhaving a pressure gain characteris tic of which at least a firstportion, as defined by a range of input pressures, is substantiallydifferent from a corresponding first portion of said predeterminednon-linear function; 1 means providing a source of fluid at constantpressure at said power nozzle; means for connecting said input signal toa first of said control nozzles; variable bias means responsive to saidinput signal for modifying said first portion of said gaincharacteristic to substantially conform to said corresponding firstportion of said predetermined non-linear function; means for connectingsaid variable bias Signal means to at least a second of said controlnozzles;

13 wherein said predetermined non-linear function .has

three portions which approximate straight lines of different slopes andwherein said variable bias means comprises: v I i I Y means comprisingtwo cascaded analog pure fluid amplifiers connected to one of saidcontrol nozzles for modifying one portion of said gain characteristic tosubstantially conform to one of said three portions of said non-linearfunction; and

means comprising another analog pure fluid amplifier connected toanother of said control nozzles for modifying another portion of saidgain characteristic to substantially conform to a second of said threeportions of said non-linear function.

9. A fluidic device for producing an output pressure signal whichresponds to a variable-pressure input signal as a predeterminednon-linear function of said input signal, comprising:

a first pure fluid amplifier comprising a power nozzle,

a plurality of control nozzles, and a plurality of output passages, andhaving a pressure gain characteristic of which at least a first portion,as defined by a range of input pressures, is substantially differentfrom a corresponding first portion of said predetermined non-linearfunction;

means providing a source of fluid at constant pressure at said powernozzle;

means for connecting said input signal to a first of said controlnozzles;

variable means responsive to said input signal for modifying said firstportion of said gain characteristic to substantially conform to saidcorresponding first portion of said predetermined non-linear function;

means for connecting said variable bias signal means to at least asecond of said control nozzles;

wherein said predetermined non-linear function is discontinuous for atleast one input pressure, and wherein said variable bias meanscomprises:

means including a bistable pure fluid amplifier connected to one of saidcontrol nozzles and responsive to said input'signal for modifying saidfirst portion of said gain characteristic and for producing adiscontinuity therein which corresponds to the discontinuity in saidpredetermined non-linear function.

10. A fluidic circuit for providing an output pressure which is apredetermined function of a variable pressure input signal, said circuitcomprising:

a first pure fluid amplifier responsive to application thereto of saidvariable pressure input signal for providing a further signal having apressure which varies as a function of said variable pressure inputsignal;

a second pure fluid amplifier responsive to simultaneous applicationthereto of said variable pressure input signal and said further signalfor providing said output pressure;

means for applying said variable pressure input signal to said first andsecond fluid amplifiers; and

means for applying said further signal to said second pure fluidamplifier.

11. A fluidic circuit for providing a fluid output signal as a functionof a fluid input signal, said circuit comprising:

first and second pure fluid amplifiers, each comprising: a power nozzleresponsive to application of pressurized fluid thereto for issuing apower stream of fluid; a first control nozzle responsive to applicationof pressurized fluid thereto for issuing a control stream in interactingrelationship with said power stream to deflect said power stream inaccordance with the pressure of the fluid applied to said controlnozzle; and at least one output passage disposed for receiving varyingportions of said power stream as a function of power stream deflection;

14 asecon d control nozzle for said second pure fluid ampli- "fierresponsive 16am 'ation "of pressurized fluid thereto for issuinga"cont"rol'st'rearn"'in interacting relationship with saidpowerstream todeflect said power stream inaccor'd'aiice with the pressure of the fluidapplied to said'seco'nd 'control nozzle; means for applyingsaidfluid-input signal to the first control no zzle of both said firstand second pure fluid amplifiers; and fluid passage means forinterconnecting said outputpassage of said first pure fluid amplifierand said' second control nozzle of said second pure fluid amplifier;wherein said fluid output signal for said circuit appears at said outputpassage of said second pure fluid amplifier. 12. The circuit accordingto claim 11 further comprising:

a third control nozzle for said second pure fluid amplifier responsiveto application of pressurized fluid thereto for issuing a control streamin interacting relationship with said power stream 'to deflect saidpower stream in accordance with the pressure of the fluid applied tosaid third control nozzle;

a third pure fluid amplifier comprising: a power nozzle responsive toapplication of pressurized fluid thereto for issuing a power stream offluid; a first control nozzle responsive to application of pressurizedfluid thereto for issuing a control stream in interacting relationshipwith said power stream to deflect said power stream in accordance withthe pressure of the fluid applied to said first control nozzle; and atleast one output passage disposed for receiving varying portions of saidpower stream as a function of power stream deflection;

means for applying said fluid input signal to said first control nozzleof said third pure fluid amplifier; and

fluid passage means for interconnecting said output passage of saidthird pure fluid amplifier and said third control nozzle of said secondpure fluid amplifier.

13. The circuit according to claim 11 further comprrsmg:

a second control nozzle for said first pure fluid amplifier responsiveto application of pressurized fluid thereto for issuing a control streamin interacting relationship with said power stream to deflect said powerstream in accordance with the pressure of the fluid applied to saidsecond control nozzle;

a third pure fluid amplifier comprising: a power nozzle responsive toapplication of pressurized fluid thereto for issuing a power stream offluid; a first control nozzle responsive to application of pressurizedfluid thereto for issuing a control stream in interacting relationshipwith said power stream to deflect said power stream in accordance withthe pressure of fluid applied to said first control nozzle; and at leastone output passage disposed for receiving varying portions of said powerstream as a function of the power stream deflection;

means for applying said fluid input signal to said first control nozzleof said third pure fluid amplifier; and

fluid passage means for interconnecting said output passage of saidthird pure fluid amplifier and said second control nozzle of said firstpure fluid amplifier.

14. The circuit according to claim 11 further comprising:

a second control nozzle for said first pure fluid amplifier responsiveto application of pressurized fluid thereto for issuing a control streamin interacting relationship with said power stream to deflect said powerstream in accordance with the pressure of the fluid applied to saidsecond control nozzle; and

means for applying a bias pressure to said second control nozzle of saidfirst pure fluid amplifier.

15 e 1a 15. The circuit according to claim 14 wherein at least 3,250,4695/1966 Colston 137-81,5 XR one of said pure fluid amplifiers isbistable. 3, 12/ 1966 C St0n 1 7-8 5 XR 3,338,515 8/1967 Dexter 13781.5XR References Cited w 3,339,571 9/1967 Hatch 1378 1.5 5 Baufil 3,155,82511/1964 Boothe 13781.5 XR SAMUEL SCOTT, Primary Examiner 3,193,1977/1965 Bauer 137-815 XR

